How Can I Select A Single Edge Among Linked Duplicates?
Actually I don't really know that in linked selection method is it even possible or not!
But I can tell you another way to achieve what you want.
You can use (shift+d) method to duplicate.
Then select all the duplicates and join them as a single object with (ctrl+ J). You can also move them individually in edit mode. But you can't move them separately in object mode,  they are all now one single object. Hope that helps.